mdw@git.distorted.org.uk Git - catacomb-python/blob - catacomb/__init__.py

   1 ### -*-python-*-
   2 ###
   3 ### Setup for Catacomb/Python bindings
   4 ###
   5 ### (c) 2004 Straylight/Edgeware
   6 ###
   7
   8 ###----- Licensing notice ---------------------------------------------------
   9 ###
  10 ### This file is part of the Python interface to Catacomb.
  11 ###
  12 ### Catacomb/Python is free software; you can redistribute it and/or modify
  13 ### it under the terms of the GNU General Public License as published by
  14 ### the Free Software Foundation; either version 2 of the License, or
  15 ### (at your option) any later version.
  16 ###
  17 ### Catacomb/Python is distributed in the hope that it will be useful,
  18 ### but WITHOUT ANY WARRANTY; without even the implied warranty of
  19 ### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  20 ### GNU General Public License for more details.
  21 ###
  22 ### You should have received a copy of the GNU General Public License
  23 ### along with Catacomb/Python; if not, write to the Free Software Foundation,
  24 ### Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
  25
  26 import _base
  27 import types as _types
  28 from binascii import hexlify as _hexify, unhexlify as _unhexify
  29 from sys import argv as _argv
  30
  31 ###--------------------------------------------------------------------------
  32 ### Basic stuff.
  33
  34 ## For the benefit of the default keyreporter, we need the program na,e.
  35 _base._ego(_argv[0])
  36
  37 ## Initialize the module.  Drag in the static methods of the various
  38 ## classes; create names for the various known crypto algorithms.
  39 def _init():
  40   d = globals()
  41   b = _base.__dict__;
  42   for i in b:
  43     if i[0] != '_':
  44       d[i] = b[i];
  45   for i in ['MP', 'GF', 'Field',
  46             'ECPt', 'ECPtCurve', 'ECCurve', 'ECInfo',
  47             'DHInfo', 'BinDHInfo', 'RSAPriv', 'BBSPriv',
  48             'PrimeFilter', 'RabinMiller',
  49             'Group', 'GE',
  50             'KeySZ', 'KeyData']:
  51     c = d[i]
  52     pre = '_' + i + '_'
  53     plen = len(pre)
  54     for j in b:
  55       if j[:plen] == pre:
  56         setattr(c, j[plen:], classmethod(b[j]))
  57   for i in [gcciphers, gchashes, gcmacs, gcprps]:
  58     for c in i.itervalues():
  59       d[c.name.replace('-', '_')] = c
  60   for c in gccrands.itervalues():
  61     d[c.name.replace('-', '_') + 'rand'] = c
  62 _init()
  63
  64 ## A handy function for our work: add the methods of a named class to an
  65 ## existing class.  This is how we write the Python-implemented parts of our
  66 ## mostly-C types.
  67 def _augment(c, cc):
  68   for i in cc.__dict__:
  69     a = cc.__dict__[i]
  70     if type(a) is _types.MethodType:
  71       a = a.im_func
  72     elif type(a) not in (_types.FunctionType, staticmethod, classmethod):
  73       continue
  74     setattr(c, i, a)
  75
  76 ## Parsing functions tend to return the object parsed and the remainder of
  77 ## the input.  This checks that the remainder is input and, if so, returns
  78 ## just the object.
  79 def _checkend(r):
  80   x, rest = r
  81   if rest != '':
  82     raise SyntaxError, 'junk at end of string'
  83   return x
  84
  85 ###--------------------------------------------------------------------------
  86 ### Bytestrings.
  87
  88 class _tmp:
  89   def fromhex(x):
  90     return ByteString(_unhexify(x))
  91   fromhex = staticmethod(fromhex)
  92   def __hex__(me):
  93     return _hexify(me)
  94   def __repr__(me):
  95     return 'bytes(%r)' % hex(me)
  96 _augment(ByteString, _tmp)
  97 bytes = ByteString.fromhex
  98
  99 ###--------------------------------------------------------------------------
 100 ### Multiprecision integers and binary polynomials.
 101
 102 def _split_rat(x):
 103   if isinstance(x, Rat): return x._n, x._d
 104   else: return x, 1
 105 class Rat (object):
 106   def __new__(cls, a, b):
 107     a, b = MP(a), MP(b)
 108     q, r = divmod(a, b)
 109     if r == 0: return q
 110     g = b.gcd(r)
 111     me = super(Rat, cls).__new__(cls)
 112     me._n = a//g
 113     me._d = b//g
 114     return me
 115   @property
 116   def numer(me): return me._n
 117   @property
 118   def denom(me): return me._d
 119   def __str__(me): return '%s/%s' % (me._n, me._d)
 120   def __repr__(me): return 'Rat(%s, %s)' % (me._n, me._d)
 121
 122   def __add__(me, you):
 123     n, d = _split_rat(you)
 124     return Rat(me._n*d + n*me._d, d*me._d)
 125   __radd__ = __add__
 126   def __sub__(me, you):
 127     n, d = _split_rat(you)
 128     return Rat(me._n*d - n*me._d, d*me._d)
 129   def __rsub__(me, you):
 130     n, d = _split_rat(you)
 131     return Rat(n*me._d - me._n*d, d*me._d)
 132   def __mul__(me, you):
 133     n, d = _split_rat(you)
 134     return Rat(me._n*n, me._d*d)
 135   def __div__(me, you):
 136     n, d = _split_rat(you)
 137     return Rat(me._n*d, me._d*n)
 138   def __rdiv__(me, you):
 139     n, d = _split_rat(you)
 140     return Rat(me._d*n, me._n*d)
 141   def __cmp__(me, you):
 142     n, d = _split_rat(you)
 143     return cmp(me._n*d, n*me._d)
 144   def __rcmp__(me, you):
 145     n, d = _split_rat(you)
 146     return cmp(n*me._d, me._n*d)
 147
 148 class _tmp:
 149   def negp(x): return x < 0
 150   def posp(x): return x > 0
 151   def zerop(x): return x == 0
 152   def oddp(x): return x.testbit(0)
 153   def evenp(x): return not x.testbit(0)
 154   def mont(x): return MPMont(x)
 155   def barrett(x): return MPBarrett(x)
 156   def reduce(x): return MPReduce(x)
 157   def __div__(me, you): return Rat(me, you)
 158   def __rdiv__(me, you): return Rat(you, me)
 159 _augment(MP, _tmp)
 160
 161 class _tmp:
 162   def zerop(x): return x == 0
 163   def reduce(x): return GFReduce(x)
 164   def trace(x, y): return x.reduce().trace(y)
 165   def halftrace(x, y): return x.reduce().halftrace(y)
 166   def modsqrt(x, y): return x.reduce().sqrt(y)
 167   def quadsolve(x, y): return x.reduce().quadsolve(y)
 168 _augment(GF, _tmp)
 169
 170 class _tmp:
 171   def product(*arg):
 172     'product(ITERABLE) or product(I, ...) -> PRODUCT'
 173     return MPMul(*arg).done()
 174   product = staticmethod(product)
 175 _augment(MPMul, _tmp)
 176
 177 ###--------------------------------------------------------------------------
 178 ### Abstract fields.
 179
 180 class _tmp:
 181   def fromstring(str): return _checkend(Field.parse(str))
 182   fromstring = staticmethod(fromstring)
 183 _augment(Field, _tmp)
 184
 185 class _tmp:
 186   def __repr__(me): return '%s(%sL)' % (type(me).__name__, me.p)
 187   def __hash__(me): return 0x114401de ^ hash(me.p)
 188   def ec(me, a, b): return ECPrimeProjCurve(me, a, b)
 189 _augment(PrimeField, _tmp)
 190
 191 class _tmp:
 192   def __repr__(me): return '%s(%sL)' % (type(me).__name__, hex(me.p))
 193   def ec(me, a, b): return ECBinProjCurve(me, a, b)
 194 _augment(BinField, _tmp)
 195
 196 class _tmp:
 197   def __hash__(me): return 0x23e4701c ^ hash(me.p)
 198 _augment(BinPolyField, _tmp)
 199
 200 class _tmp:
 201   def __hash__(me):
 202     h = 0x9a7d6240
 203     h ^=   hash(me.p)
 204     h ^= 2*hash(me.beta) & 0xffffffff
 205     return h
 206 _augment(BinNormField, _tmp)
 207
 208 class _tmp:
 209   def __str__(me): return str(me.value)
 210   def __repr__(me): return '%s(%s)' % (repr(me.field), repr(me.value))
 211 _augment(FE, _tmp)
 212
 213 ###--------------------------------------------------------------------------
 214 ### Elliptic curves.
 215
 216 class _tmp:
 217   def __repr__(me):
 218     return '%s(%r, %s, %s)' % (type(me).__name__, me.field, me.a, me.b)
 219   def frombuf(me, s):
 220     return ecpt.frombuf(me, s)
 221   def fromraw(me, s):
 222     return ecpt.fromraw(me, s)
 223   def pt(me, *args):
 224     return me(*args)
 225 _augment(ECCurve, _tmp)
 226
 227 class _tmp:
 228   def __hash__(me):
 229     h = 0x6751d341
 230     h ^=   hash(me.field)
 231     h ^= 2*hash(me.a) ^ 0xffffffff
 232     h ^= 5*hash(me.b) ^ 0xffffffff
 233     return h
 234 _augment(ECPrimeCurve, _tmp)
 235
 236 class _tmp:
 237   def __hash__(me):
 238     h = 0x2ac203c5
 239     h ^=   hash(me.field)
 240     h ^= 2*hash(me.a) ^ 0xffffffff
 241     h ^= 5*hash(me.b) ^ 0xffffffff
 242     return h
 243 _augment(ECBinCurve, _tmp)
 244
 245 class _tmp:
 246   def __repr__(me):
 247     if not me: return 'ECPt()'
 248     return 'ECPt(%s, %s)' % (me.ix, me.iy)
 249   def __str__(me):
 250     if not me: return 'inf'
 251     return '(%s, %s)' % (me.ix, me.iy)
 252 _augment(ECPt, _tmp)
 253
 254 class _tmp:
 255   def __repr__(me):
 256     return 'ECInfo(curve = %r, G = %r, r = %s, h = %s)' % \
 257            (me.curve, me.G, me.r, me.h)
 258   def __hash__(me):
 259     h = 0x9bedb8de
 260     h ^=   hash(me.curve)
 261     h ^= 2*hash(me.G) & 0xffffffff
 262     return h
 263   def group(me):
 264     return ECGroup(me)
 265 _augment(ECInfo, _tmp)
 266
 267 class _tmp:
 268   def __repr__(me):
 269     if not me: return '%r()' % (me.curve)
 270     return '%r(%s, %s)' % (me.curve, me.x, me.y)
 271   def __str__(me):
 272     if not me: return 'inf'
 273     return '(%s, %s)' % (me.x, me.y)
 274 _augment(ECPtCurve, _tmp)
 275
 276 ###--------------------------------------------------------------------------
 277 ### Key sizes.
 278
 279 class _tmp:
 280   def __repr__(me): return 'KeySZAny(%d)' % me.default
 281   def check(me, sz): return True
 282   def best(me, sz): return sz
 283 _augment(KeySZAny, _tmp)
 284
 285 class _tmp:
 286   def __repr__(me):
 287     return 'KeySZRange(%d, %d, %d, %d)' % \
 288            (me.default, me.min, me.max, me.mod)
 289   def check(me, sz): return me.min <= sz <= me.max and sz % me.mod == 0
 290   def best(me, sz):
 291     if sz < me.min: raise ValueError, 'key too small'
 292     elif sz > me.max: return me.max
 293     else: return sz - (sz % me.mod)
 294 _augment(KeySZRange, _tmp)
 295
 296 class _tmp:
 297   def __repr__(me): return 'KeySZSet(%d, %s)' % (me.default, me.set)
 298   def check(me, sz): return sz in me.set
 299   def best(me, sz):
 300     found = -1
 301     for i in me.set:
 302       if found < i <= sz: found = i
 303     if found < 0: raise ValueError, 'key too small'
 304     return found
 305 _augment(KeySZSet, _tmp)
 306
 307 ###--------------------------------------------------------------------------
 308 ### Abstract groups.
 309
 310 class _tmp:
 311   def __repr__(me):
 312     return '%s(p = %s, r = %s, g = %s)' % \
 313            (type(me).__name__, me.p, me.r, me.g)
 314 _augment(FGInfo, _tmp)
 315
 316 class _tmp:
 317   def group(me): return PrimeGroup(me)
 318 _augment(DHInfo, _tmp)
 319
 320 class _tmp:
 321   def group(me): return BinGroup(me)
 322 _augment(BinDHInfo, _tmp)
 323
 324 class _tmp:
 325   def __repr__(me):
 326     return '%s(%r)' % (type(me).__name__, me.info)
 327 _augment(Group, _tmp)
 328
 329 class _tmp:
 330   def __hash__(me):
 331     info = me.info
 332     h = 0xbce3cfe6
 333     h ^=   hash(info.p)
 334     h ^= 2*hash(info.r) & 0xffffffff
 335     h ^= 5*hash(info.g) & 0xffffffff
 336     return h
 337 _augment(PrimeGroup, _tmp)
 338
 339 class _tmp:
 340   def __hash__(me):
 341     info = me.info
 342     h = 0x80695949
 343     h ^=   hash(info.p)
 344     h ^= 2*hash(info.r) & 0xffffffff
 345     h ^= 5*hash(info.g) & 0xffffffff
 346     return h
 347 _augment(BinGroup, _tmp)
 348
 349 class _tmp:
 350   def __hash__(me): return 0x0ec23dab ^ hash(me.info)
 351 _augment(ECGroup, _tmp)
 352
 353 class _tmp:
 354   def __repr__(me):
 355     return '%r(%r)' % (me.group, str(me))
 356 _augment(GE, _tmp)
 357
 358 ###--------------------------------------------------------------------------
 359 ### RSA encoding techniques.
 360
 361 class PKCS1Crypt (object):
 362   def __init__(me, ep = '', rng = rand):
 363     me.ep = ep
 364     me.rng = rng
 365   def encode(me, msg, nbits):
 366     return _base._p1crypt_encode(msg, nbits, me.ep, me.rng)
 367   def decode(me, ct, nbits):
 368     return _base._p1crypt_decode(ct, nbits, me.ep, me.rng)
 369
 370 class PKCS1Sig (object):
 371   def __init__(me, ep = '', rng = rand):
 372     me.ep = ep
 373     me.rng = rng
 374   def encode(me, msg, nbits):
 375     return _base._p1sig_encode(msg, nbits, me.ep, me.rng)
 376   def decode(me, msg, sig, nbits):
 377     return _base._p1sig_decode(msg, sig, nbits, me.ep, me.rng)
 378
 379 class OAEP (object):
 380   def __init__(me, mgf = sha_mgf, hash = sha, ep = '', rng = rand):
 381     me.mgf = mgf
 382     me.hash = hash
 383     me.ep = ep
 384     me.rng = rng
 385   def encode(me, msg, nbits):
 386     return _base._oaep_encode(msg, nbits, me.mgf, me.hash, me.ep, me.rng)
 387   def decode(me, ct, nbits):
 388     return _base._oaep_decode(ct, nbits, me.mgf, me.hash, me.ep, me.rng)
 389
 390 class PSS (object):
 391   def __init__(me, mgf = sha_mgf, hash = sha, saltsz = None, rng = rand):
 392     me.mgf = mgf
 393     me.hash = hash
 394     if saltsz is None:
 395       saltsz = hash.hashsz
 396     me.saltsz = saltsz
 397     me.rng = rng
 398   def encode(me, msg, nbits):
 399     return _base._pss_encode(msg, nbits, me.mgf, me.hash, me.saltsz, me.rng)
 400   def decode(me, msg, sig, nbits):
 401     return _base._pss_decode(msg, sig, nbits,
 402                              me.mgf, me.hash, me.saltsz, me.rng)
 403
 404 class _tmp:
 405   def encrypt(me, msg, enc):
 406     return me.pubop(enc.encode(msg, me.n.nbits))
 407   def verify(me, msg, sig, enc):
 408     if msg is None: return enc.decode(msg, me.pubop(sig), me.n.nbits)
 409     try:
 410       x = enc.decode(msg, me.pubop(sig), me.n.nbits)
 411       return x is None or x == msg
 412     except ValueError:
 413       return False
 414 _augment(RSAPub, _tmp)
 415
 416 class _tmp:
 417   def decrypt(me, ct, enc): return enc.decode(me.privop(ct), me.n.nbits)
 418   def sign(me, msg, enc): return me.privop(enc.encode(msg, me.n.nbits))
 419 _augment(RSAPriv, _tmp)
 420
 421 ###--------------------------------------------------------------------------
 422 ### Built-in named curves and prime groups.
 423
 424 class _groupmap (object):
 425   def __init__(me, map, nth):
 426     me.map = map
 427     me.nth = nth
 428     me.i = [None] * (max(map.values()) + 1)
 429   def __repr__(me):
 430     return '{%s}' % ', '.join(['%r: %r' % (k, me[k]) for k in me])
 431   def __contains__(me, k):
 432     return k in me.map
 433   def __getitem__(me, k):
 434     i = me.map[k]
 435     if me.i[i] is None:
 436       me.i[i] = me.nth(i)
 437     return me.i[i]
 438   def __setitem__(me, k, v):
 439     raise TypeError, "immutable object"
 440   def __iter__(me):
 441     return iter(me.map)
 442   def iterkeys(me):
 443     return iter(me.map)
 444   def itervalues(me):
 445     for k in me:
 446       yield me[k]
 447   def iteritems(me):
 448     for k in me:
 449       yield k, me[k]
 450   def keys(me):
 451     return [k for k in me]
 452   def values(me):
 453     return [me[k] for k in me]
 454   def items(me):
 455     return [(k, me[k]) for k in me]
 456 eccurves = _groupmap(_base._eccurves, ECInfo._curven)
 457 primegroups = _groupmap(_base._pgroups, DHInfo._groupn)
 458 bingroups = _groupmap(_base._bingroups, BinDHInfo._groupn)
 459
 460 ###--------------------------------------------------------------------------
 461 ### Prime number generation.
 462
 463 class PrimeGenEventHandler (object):
 464   def pg_begin(me, ev):
 465     return me.pg_try(ev)
 466   def pg_done(me, ev):
 467     return PGEN_DONE
 468   def pg_abort(me, ev):
 469     return PGEN_TRY
 470   def pg_fail(me, ev):
 471     return PGEN_TRY
 472   def pg_pass(me, ev):
 473     return PGEN_TRY
 474
 475 class SophieGermainStepJump (object):
 476   def pg_begin(me, ev):
 477     me.lf = PrimeFilter(ev.x)
 478     me.hf = me.lf.muladd(2, 1)
 479     return me.cont(ev)
 480   def pg_try(me, ev):
 481     me.step()
 482     return me.cont(ev)
 483   def cont(me, ev):
 484     while me.lf.status == PGEN_FAIL or me.hf.status == PGEN_FAIL:
 485       me.step()
 486     if me.lf.status == PGEN_ABORT or me.hf.status == PGEN_ABORT:
 487       return PGEN_ABORT
 488     ev.x = me.lf.x
 489     if me.lf.status == PGEN_DONE and me.hf.status == PGEN_DONE:
 490       return PGEN_DONE
 491     return PGEN_TRY
 492   def pg_done(me, ev):
 493     del me.lf
 494     del me.hf
 495
 496 class SophieGermainStepper (SophieGermainStepJump):
 497   def __init__(me, step):
 498     me.lstep = step;
 499     me.hstep = 2 * step
 500   def step(me):
 501     me.lf.step(me.lstep)
 502     me.hf.step(me.hstep)
 503
 504 class SophieGermainJumper (SophieGermainStepJump):
 505   def __init__(me, jump):
 506     me.ljump = PrimeFilter(jump);
 507     me.hjump = me.ljump.muladd(2, 0)
 508   def step(me):
 509     me.lf.jump(me.ljump)
 510     me.hf.jump(me.hjump)
 511   def pg_done(me, ev):
 512     del me.ljump
 513     del me.hjump
 514     SophieGermainStepJump.pg_done(me, ev)
 515
 516 class SophieGermainTester (object):
 517   def __init__(me):
 518     pass
 519   def pg_begin(me, ev):
 520     me.lr = RabinMiller(ev.x)
 521     me.hr = RabinMiller(2 * ev.x + 1)
 522   def pg_try(me, ev):
 523     lst = me.lr.test(ev.rng.range(me.lr.x))
 524     if lst != PGEN_PASS and lst != PGEN_DONE:
 525       return lst
 526     rst = me.hr.test(ev.rng.range(me.hr.x))
 527     if rst != PGEN_PASS and rst != PGEN_DONE:
 528       return rst
 529     if lst == PGEN_DONE and rst == PGEN_DONE:
 530       return PGEN_DONE
 531     return PGEN_PASS
 532   def pg_done(me, ev):
 533     del me.lr
 534     del me.hr
 535
 536 class PrimitiveStepper (PrimeGenEventHandler):
 537   def __init__(me):
 538     pass
 539   def pg_try(me, ev):
 540     ev.x = me.i.next()
 541     return PGEN_TRY
 542   def pg_begin(me, ev):
 543     me.i = iter(smallprimes)
 544     return me.pg_try(ev)
 545
 546 class PrimitiveTester (PrimeGenEventHandler):
 547   def __init__(me, mod, hh = [], exp = None):
 548     me.mod = MPMont(mod)
 549     me.exp = exp
 550     me.hh = hh
 551   def pg_try(me, ev):
 552     x = ev.x
 553     if me.exp is not None:
 554       x = me.mod.exp(x, me.exp)
 555       if x == 1: return PGEN_FAIL
 556     for h in me.hh:
 557       if me.mod.exp(x, h) == 1: return PGEN_FAIL
 558     ev.x = x
 559     return PGEN_DONE
 560
 561 class SimulStepper (PrimeGenEventHandler):
 562   def __init__(me, mul = 2, add = 1, step = 2):
 563     me.step = step
 564     me.mul = mul
 565     me.add = add
 566   def _stepfn(me, step):
 567     if step <= 0:
 568       raise ValueError, 'step must be positive'
 569     if step <= MPW_MAX:
 570       return lambda f: f.step(step)
 571     j = PrimeFilter(step)
 572     return lambda f: f.jump(j)
 573   def pg_begin(me, ev):
 574     x = ev.x
 575     me.lf = PrimeFilter(x)
 576     me.hf = PrimeFilter(x * me.mul + me.add)
 577     me.lstep = me._stepfn(me.step)
 578     me.hstep = me._stepfn(me.step * me.mul)
 579     SimulStepper._cont(me, ev)
 580   def pg_try(me, ev):
 581     me._step()
 582     me._cont(ev)
 583   def _step(me):
 584     me.lstep(me.lf)
 585     me.hstep(me.hf)
 586   def _cont(me, ev):
 587     while me.lf.status == PGEN_FAIL or me.hf.status == PGEN_FAIL:
 588       me._step()
 589     if me.lf.status == PGEN_ABORT or me.hf.status == PGEN_ABORT:
 590       return PGEN_ABORT
 591     ev.x = me.lf.x
 592     if me.lf.status == PGEN_DONE and me.hf.status == PGEN_DONE:
 593       return PGEN_DONE
 594     return PGEN_TRY
 595   def pg_done(me, ev):
 596     del me.lf
 597     del me.hf
 598     del me.lstep
 599     del me.hstep
 600
 601 class SimulTester (PrimeGenEventHandler):
 602   def __init__(me, mul = 2, add = 1):
 603     me.mul = mul
 604     me.add = add
 605   def pg_begin(me, ev):
 606     x = ev.x
 607     me.lr = RabinMiller(x)
 608     me.hr = RabinMiller(x * me.mul + me.add)
 609   def pg_try(me, ev):
 610     lst = me.lr.test(ev.rng.range(me.lr.x))
 611     if lst != PGEN_PASS and lst != PGEN_DONE:
 612       return lst
 613     rst = me.hr.test(ev.rng.range(me.hr.x))
 614     if rst != PGEN_PASS and rst != PGEN_DONE:
 615       return rst
 616     if lst == PGEN_DONE and rst == PGEN_DONE:
 617       return PGEN_DONE
 618     return PGEN_PASS
 619   def pg_done(me, ev):
 620     del me.lr
 621     del me.hr
 622
 623 def sgprime(start, step = 2, name = 'p', event = pgen_nullev, nsteps = 0):
 624   start = MP(start)
 625   return pgen(start, name, SimulStepper(step = step), SimulTester(), event,
 626               nsteps, RabinMiller.iters(start.nbits))
 627
 628 def findprimitive(mod, hh = [], exp = None, name = 'g', event = pgen_nullev):
 629   return pgen(0, name, PrimitiveStepper(), PrimitiveTester(mod, hh, exp),
 630               event, 0, 1)
 631
 632 def kcdsaprime(pbits, qbits, rng = rand,
 633                event = pgen_nullev, name = 'p', nsteps = 0):
 634   hbits = pbits - qbits
 635   h = pgen(rng.mp(hbits, 1), name + ' [h]',
 636            PrimeGenStepper(2), PrimeGenTester(),
 637            event, nsteps, RabinMiller.iters(hbits))
 638   q = pgen(rng.mp(qbits, 1), name, SimulStepper(2 * h, 1, 2),
 639            SimulTester(2 * h, 1), event, nsteps, RabinMiller.iters(qbits))
 640   p = 2 * q * h + 1
 641   return p, q, h
 642
 643 #----- That's all, folks ----------------------------------------------------